Finite Group DatabasebetaFinite Group Databasebeta| order | 19044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D529 |
| unambiguous semidirect product | (C3×D529)⋊D3 |
| Fitting, derived, Hall | C32×C529 ⋊ C22 |
| Sylow | C529 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C529 | C22 |
| Frattini | C23 | C3⋊D3×D23 |
| socle | C32×C23 | C2×D23 |
| LCS | G ▷ C32×C529 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4761 |
1596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19044, 21);